Tree-Structured Methods for Prediction and Data Visualization

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

Though many recursive partitioning algorithms exist in the literature, most are unsuitable for model interpretation because they tend to select some types of predictor variables more frequently than others. As a result, such tree structures can yield misleading conclusions about the roles and relative importance of the predictor variables. The main thrust of the proposed research is to extend the investigator's GUIDE and QUEST strategies to regression and classification, respectively. This approach effectively solves the problem of selection bias and significantly reduces computation time. The computational savings make it feasible to build tree-structured models that are hitherto impractical to construct. A second objective is to use the methods to model unreplicated and fractionally replicated data from designed experiments. The hierarchical structure of tree-structured models and their variable selection ability make them attractive alternatives to traditional methods. A third objective is extension of the investigator's LOTUS algorithm to fit logistic regression trees to data with multinomial response variables. Statistical models constructed from high-dimensional data are often difficult or unintuitive to interpret. This applies even to the simplest model, the multiple linear regression model, where interpretation of the parameter estimates is fraught with difficulties caused by nonlinearity, multicollinearity, and interactions in the data. Graphical visualization is perhaps the most effective way to interpret a model. But such techniques are inapplicable to more than two or three dimensions. The proposed research enables the application of visualization techniques to high-dimensional data by using a tree-structured method to partition the data space such that at most one, two, or three predictor variables are needed to model the data in each partition. The result is a graphical model whose broad features are representable by a tree structure and whose finer features are visualizable by two and three-dimensional graphical displays.